Calculus in Motion: From Incremental to Continuous

The author has taught mathematics at U.S. universities for over 25 years. This book grew directly out of that classroom experience: it has been in continuous use with students and is regularly revised based on their needs and feedback. Its main goal is to deepen the reader's understanding rather than to prepare for any specific exam.This textbook is intended for a streamlined one-semester calculus course.Calculus is the science of change, but it is more narrowly a study of motion.From the very beginning of calculus, its peculiar challenge has been to study continuous motion. Skillful manipulation of those formulas is what solves calculus problems. We take a different approach.Initially, we limit ourselves to incremental phenomena and the quantities indivisible by their very nature: people, animals, and other organisms, moments of time, locations of space, particles, some commodities, digital images and other man-made data, etc. Computers excel at handling these incremental processes.Later, we supplement the incremental part with a study of continuous phenomena and the quantities infinitely divisible either by their nature or by assumption: time, space, mass, temperature, money, some commodities, etc.The order is opposite to that of the traditional approach, which relies on discretization:Motion through multi-dimensional spaces is considered in parallel.CONTENTSChapter 1: The differences and the sumsChapter 2: The difference quotients and the Riemann sumsChapter 3: The derivatives and the integralsChapter 4: Limits and continuityChapter 5: Additional topics Read more